The Effect of Jupiter’s Mass on Earth’s Orbit

1. The Effect of Jupiter’s Mass on Earth’s Orbit Also Distance/Velocity Tests to Observe When an Asteroid Falls Into Orbit Anthony White

2. Purpose • First to find the dependence of Earths orbit on the mass and relative distance of Jupiter • Second to find out what it takes to put a traveling asteroid into orbit by changing the velocity, distance and mass

3. How this is Accomplished • Python Program • Newton’s Laws • Accurate masses, velocities and distances • Leapfrog Acceleration • User Prompts

4. Explanation • Theory of Gravity Established by Newton • Take Note: Seasons determined by 23.5 degree tilt, not distance from the sun

5. Main Equation • Force Created (Inverse Square Law): • Where m1 and m2 are two masses and r is the distance between

6. Effects of Elliptical Orbit on Earth? • Well, not many • Sunlight falling during the perihelion is about 7% more intense • However, the northern hemisphere has more land, while the southern hemisphere has more water, which makes only a moderate impact on the differences between perihelion and aphelion

7. Results (Jupiter Effect) • First, Testing the Orbit with Jupiter having zero mass: • Notice: Immediately Falls into Circular Orbit

8. Results (Jupiter Effect) • Next, the Orbit with Jupiter being the mass it is now: • Notice Extremely Similar Orbital Pattern (Near Circular Orbit)

9. Results (Jupiter Effect) • Next, the Orbit with Jupiter’s mass being 100 times greater: • Notice: Height of Curve has increased due to greater eccentricity. Also notice the graph on the distance from the sun shows this elliptical effect.

10. Results (Jupiter Effect) • Next, the Orbit with Jupiter’s mass being 500 times greater: • Notice: Greater Eccentricity still, as well as that ellipse itself is rotating around the sun (following Jupiter’s orbit)

11. Results (Jupiter Effect) • Rotating Elliptical Orbit when Jupiter’s Mass is Multiplied by 500 • Notice: Elliptical Shift

12. Results (Jupiter Effect) • Earth’s Orbit when Jupiter’s Mass is Multiplied by 1000 • Notice: Gravitational attraction from Jupiter great enough to pull earth out of the orbit

13. Results (Jupiter Effect) • Earth’s Orbit when distance was halved: • Notice: Similar Orbit created (very close to circular)

14. Results (Asteroid) • “Average” Asteroid Properties (averaging the properties of about 100 Asteroids data was found on) • At the same distance each time:

15. Results (Asteroid) • At average velocity and a set distance • Notice: It gets pulled into an elliptical orbit as well

16. Results (Asteroid) • At half velocity and a set distance • Notice: It gets pulled into an elliptical orbit as well, except it is much thinner

17. Results (Asteroid) • At quarter velocity and a set distance • Notice: It gets pulled into an elliptical orbit that is even still tighter (also notice the ellipse is beginning to shift)

18. Results (Asteroid) • At double velocity from same distance: • Notice: This is above the escape velocity needed to escape the simple solar system

19. Conclusion (Jupiter’s Mass) • As the mass of Jupiter is increased, the orbit of the Earth goes from being more circular to elliptical • Also that elliptical rotation itself will begin to shift around the sun as it follows Jupiter • If the mass is increased too much the Earth will eventually escape the pull from the Sun

20. Conclusion (Asteroid) • As the velocity is lower, the ellipse that is created decreases more and more in width. • It also still shifts around the sun • If the velocity is doubled then it is above escape velocity for the attraction from the Sun, Earth and Jupiter